Editor’s Note: The following is an excerpt from Norm Zadeh's new book Hold’em Poker Super Strategy.
Publisher’s Note: For those who don't know, Zadeh’s original 1974 book Winning Poker Systems was the first poker book that explained and relied on game theory to develop a strategy. It concentrated mainly on lowball draw but this article and his new book is about hold ’em. We have not yet looked at the complete book but the excerpt seems quite interesting though perhaps controversial. It concerns the big blind, on the flop, betting right into the preflop raiser and caller. A play he says is often right with second pair, quality kicker. Zadeh is a Ph.D. in computer science and his first book was excellent. So, his conclusions should not be dismissed even if they disagree with most of today’s experts. (Our first inclination is that he may have underestimated the relevance of future bets. But maybe not.)
We at Two Plus Two invite serious players to weigh in regarding this excerpt. They can do so on our Magazine Forum, our Books and Publication Forum, or elsewhere.
What follows is a modification of some hopefully useful material from Chapter 20 of my new book, Hold’em Poker Super Strategy. A question that comes up a lot, is what to do if you’re the big blind in a three player contest, are first-to-act, and make a reasonable hand like middle pair, top kicker? Do you check or bet? To answer this question, assume you are playing in a $5-10 game. Everyone folds to the player in position 5 (five players act after he does) who opens for $25 into a pot of $15. We will assume that he is following my recommended opening strategy from Chapter 4 and has a range of A9 or better or equivalent. That means, according to Chapter 3, that his range is A8s+, A9o+, KQo, KJs+, and 22+. The dealer calls with A7-AJ, and you call in the big blind with A7-AJ. By “A7 to AJ” I mean A7o–AJo, A2s–ATs, 22–77, KJo–KQo, KTs, and QJs, which has a 13% chance of occurring (Poker Cruncher). This range is looser than what I recommend in Chapter 5 for the big blind but appears to be closer to what many players call with.
To keep things simple, I will assume that each bet made on the flop is ½ pot. If you are first-to-act, you will be faced with two key questions: 1) Is my hand good enough to bet ½ pot, and 2) would I do better by checking? As we will see, if your hand is good enough to bet, unless it is an absolute monster, it will virtually always be better to bet than check. We will initially make that assumption and demonstrate its correctness later.
Chances needed by first-to-act to bet ½ pot
In a three-player contest, each player will have, on average, around a 1 in 3 (33%) chance of winning. However, because there is often an advantage in leading with a ½ pot bet, we will initially assume that first-to-act needs a 31% chance of winning to bet ½ pot and then analyze a few hands to verify the accuracy of that assumption. Table 20.1 provides the chances of the big blind winning with various hands and flops. I computed Table 20.1 for two different ranges. The column that is of particular relevance to this article, is the column entitled “CHANCES vs A9+, A7-AJ”, because those are the ranges assumed here. The right-most column assumes that your opponents have somewhat weaker ranges, A7 or better, but not better than A9. Specifically, I assumed those ranges were A7-A9o, A2–A9s, 22–66, KT–KQo, K9s, QT–QJ, JT, Q9s, J9s, T8s–T9s, 98s, and 87s, which make up 16.7% of all hands. These ranges are weaker than what I recommend but are close to what many players call with.
The second column from the right, which corresponds to our assumed ranges, shows that first-to-act has greater than a 31% chance in many instances, and should lead by betting ½ pot with pretty much all top pairs, as well as some middle pairs and even a few bottom pairs.1 To better understand why, suppose P5 (the player in position 5 with five players who act after he does) opened with A9 or better, the dealer called with A7 to AJ, you called in the big blind with A
9
, and the flop is Q
9
4. With these assumptions, the ninth row of Table 20.1 in the middle pair section indicates that your A9 has a 41% chance of winning. Based on our assumed 31% requirement, that would be enough. But what really matters is what is likely to happen after you bet ½ pot, which in turn is related to the likelihood that either of your opponents has a better hand. To compute that probability, we need to determine the distribution of your opponent’s hands. Table 20.2 provides that information. To obtain Table 20.2, I inputted the flop, your hole cards, and your opponent’s assumed distributions, into Flopzilla.
The probability that P5 has a better hand than your A9 is provided by the middle column of Table 20.2. It is 5.2% + 6.7% + 15.7% + 9% + ½ x 4.5% = 38.8%. The probability that the dealer has a better hand than you do is provided by the right column of Table 20.2. It is 2.3% + 11.3% + ½ x 4.5% = 15.8%. The probability that neither player has better than your A9 is thus (1 - .388) x (1 - .158) = 51.5%. Our conclusion is that a hand that has a 41% chance of winning in a showdown (Table 20.1) has closer to a 51% chance of being best on the flop.
What hands should players call with?
What hands should opponents call you with, if they believe that your ½ pot bet shows at least middle pair? To answer this question, we need to estimate the chances your opponents need to call. Assume that the pot is $80, you bet $40, and anyone who calls will have to invest an additional $60 on top of the $40. In this case, the caller will be risking $100 to win $180, and will need roughly a 100/(100+180) = 36% chance of winning. Because your opponents will have superior position, we will reduce that requirement to 31% and see where it takes us.
When the big blind leads with a ½ pot bet, the next player to act (the opener) will have two issues. First, most players who lead in the big blind position in a three-player contest will have at least middle pair. Second, even if the opener has a 31% chance against the player with middle pair or better, the opener should be concerned about last-to-act having a better hand than he does. Table 20.3 was created to deal with these issues. It provides the chances of the opener beating the big blind and the player yet to act, if the big blind has middle pair or better. It also provides the chances of last-to-act beating the big blind if the opener folds.
To see how Table 20.3 can be used, consider the above flop of Q 9 4. The big blind leads with a ½ pot bet, presumably with middle pair or better. The opener has A9 offsuit. Should the opener call? That question is answered by the cell containing A9 on the right side of row eleven of Table 20.3. It indicates that the opener only has a 21% of winning, which is far below the 31% chance he needs. If the opener folds, the same cell indicates that last-to-act would have a 28% chance with that same hand, also not enough. Now suppose the opener has TT. The numbers 28% and 37% corresponding to the cell containing “TT” in that same row, indicate that the opener should fold TT, but last-to-act should call with that hand.
How often will the big blind’s opponents be calling?
If the big blind’s opponents follow Table 20.3 after the big blind bets ½ pot, the opener will fold with TT or less, or 67.9% of the time (Table 20.2), and last-to-act will fold 86.4% of the time. Together, they will fold .679 x .864 = 58.7% of the time, making it very profitable for the big blind to lead by betting ½ pot with his entire range.
This analysis has several important consequences. First, if the big blind’s opponents trust him to have a hand when he bets, then the big blind will do much better by betting than checking with middle pair top kicker. If he checks, he will have at best a 41% chance (Table 20.1, middle pair, row 9). If he bets, he will have at least a 58.7% chance. If he bets, he has a good chance of winning the pot right there, or at least getting an opponent who could outdraw him to fold. If he checks, his chances will likely decrease on the turn. The problem for his opponents is that if they fold this frequently, the big blind will gain by betting 1/2 pot with his entire range.
Table 20.3 shows that calling with two high cards and no pair is a bad idea. For example, the eighth row of Table 20.3 indicates if the flop is K 5 2 and you hold AQ, you will only have between an 8% and a 12% chance of winning. Row twelve shows that with a flop Q 9 4, if you have AK offsuit, you will only have between a 10% and a 13% chance of winning. Small pocket pairs like 88 and 66 should also be hurled into the trash can as they typically have only around a 12% chance of winning (see Table 20.3, rows 2, 4, 6, 10, 12, and 13).
1 For the sake of computational simplicity, I will assume that first-to-act bets with trips as well even though it may be better to slowplay such hands. This assumption will rarely affect the minimum betting hands, and if it does, only to a minor degree.
Norm Zadeh has written two books on poker, Hold’em Poker Super Strategy, which just came out and is available through Amazon and Winning Poker Systems, which was published in 1974 and is gathering dust.
A former professional gambler, former poker editor for Gambling Times Magazine, and hedge fund manager, Norm taught as a professor at Stanford, UCLA, Columbia, and U.C. Irvine in the seventies and eighties.
In 1996, he began publishing the magazine, Perfect 10, which featured tasteful images of scantily clad top natural models, including Victoria’s Secret’s Marisa Miller. Norm ended up losing most his money trying to save Perfect 10 from unrelenting copyright infringement.
He is back to his true love, poker, which he was playing almost every day at Hollywood Park, with substantial success, until the pandemic hit.
